Department of Biostatistics, Johns Hopkins School of Public Health
For each second and each person:
Obtain joint distribution of acceleration and lag acceleration for a series of lags
Calculate scalar summaries of the joint distribution
I will walk through the process for one second, one person, and one lag
Intuition: walking is cyclic process. We want to leverage cyclic nature of walking.
Hat tip to Edward Gunning for the idea for these figures
Hat tip to Edward Gunning for the idea for these figures
Hat tip to Edward Gunning for the idea for these figures
Hat tip to Edward Gunning for the idea for these figures
\[\text{logit}(p_{ij}^{i_0}) =\beta_0^{i_0} + \int_{u=1}^S\int_{s=u}^SF_{i_0}\{ v_{ij}(s), v_{ij}(s-u), u\}dsdu \]
\(u = 1, \dots, S = 100\) (number of observations per second)
\(v_{ij}(s)\) = acceleration at centisecond \(s\) for subject \(i\) in second \(j\)
\(F(\cdot, \cdot, \cdot)\): trivariate smooth function
Hat tip to Edward Gunning for the idea for these figures
Rank-1 (rank-5) % accuracies
153 person dataset
3 min of walking seach
Two sessions at least 1 week apart
5 open source algorithms, 3 datasets with gold-standard step counts
How many steps does the average American take per day?
Is taking more steps better for you?
Do males take more steps than females? At what points during the day?
Implementation: Fast univariate inference (FUI) Cui et al. (2021) \[\mathbb{E}[\mathrm{steps}_i(s)] = \beta_0(s) + \beta_1(s)\mathrm{gender}_i + \beta_2(s)\mathrm{age}_i \]
\(i\): participant
\(s \in \{1, \dots, 1440\}\): each minute of the day
Fit separate GLM at each point \(s\) and smooth the resulting point estimates to get estimated effect of age, sex on steps profile
Bootstrap subjects to get confidence bands
Implementation: Fast univariate inference (FUI) Cui et al. (2021) \[\mathbb{E}[\mathrm{steps}_i(s)] = \beta_0(s) + \beta_1(s)\mathrm{gender}_i + \beta_2(s)\mathrm{age}_i \]
\(i\): participant
\(s \in \{1, \dots, 1440\}\): each minute of the day
Fit separate GLM at each point \(s\) and smooth the resulting point estimates to get estimated effect of age, sex on steps profile
Bootstrap subjects to get confidence bands
BUT: NHANES is not a simple random sample
Individuals are sampled in geographic clusters
Minority groups are oversampled
Are our estimates valid for population-level inference?
Implementation: Fast univariate inference (FUI) Cui et al. (2021) \[\mathbb{E}[\mathrm{steps}_i(s)] = \beta_0(s) + \beta_1(s)\mathrm{gender}_i + \beta_2(s)\mathrm{age}_i \]
\(i\): participant
\(s \in \{1, \dots, 1440\}\): each minute of the day
Fit separate GLM at each point \(s\) and smooth the resulting point estimates to get estimated effect of age, sex on steps profile
Bootstrap subjects to get confidence bands
BUT: NHANES is not a simple random sample
Individuals are sampled in geographic clusters
Minority groups are oversampled
Are our estimates valid for population-level inference?
For standard regression: \(\texttt{svyglm}\), \(\texttt{svycoxph}\)
Implementation: Fast univariate inference (FUI) Cui et al. (2021) \[\mathbb{E}[\mathrm{steps}_i(s)] = \beta_0(s) + \beta_1(s)\mathrm{gender}_i + \beta_2(s)\mathrm{age}_i \]
\(i\): participant
\(s \in \{1, \dots, 1440\}\): each minute of the day
Fit separate GLM at each point \(s\) and smooth the resulting point estimates to get estimated effect of age, sex on steps profile
Bootstrap subjects to get confidence bands
BUT: NHANES is not a simple random sample
Individuals are sampled in geographic clusters
Minority groups are oversampled
Are our estimates valid for population-level inference?
For standard regression: \(\texttt{svyglm}\), \(\texttt{svycoxph}\)
For functional regression: ?
\[\mathbb{E}[\mathrm{steps}_i(s)] = \beta_0(s) + \beta_1(s)\mathrm{gender}_i + \beta_2(s)\mathrm{age}_i \]
\(i\): participant
\(s \in \{1, \dots, 1440\}\): each minute of the day
\(\beta_0(s)\): mean steps over the course of the day taken for males age 0
\(\beta_1(s)\): how many additional steps do females take compared to males, over the course of the day, controlling for age?